A*

B*

C*

Euler line

X_{2574}

X_{2575}

C = (15.331596510458281, 17.159008739912707)
B = (22.585402740439793, -4.668952822995226)
A = (-3.9669124574672026, -3.5717497156436946)
r = AngularBisector(B, A, C)
X_{1113} = TriangleCenter(A, B, C, 1113)
F = Mirror(X_{1113}, r)
v = Vector(A, F)
X_{155} = TriangleCenter(A, B, C, 155)
t = Line(X_{155}, v)
polígono1, c, a, b = Polygon(A, B, C)
P = (11.396453236614066, -1.0482265861385707)
polígono2, A', B', C' = TrianguloPedal(A, B, C, P)
A_1 = Midpoint(a)
B_1 = Midpoint(b)
C_1 = Midpoint(c)
A_2 = Midpoint(B', C')
B_2 = Midpoint(C', A')
C_2 = Midpoint(B', A')
polígono3, f, d, e = Polygon(A_1, B_1, C_1)
polígono4, i, g, h = Polygon(A_2, B_2, C_2)
D' = Mirror(A_1, A_2)
E' = Mirror(B_1, B_2)
F' = Mirror(C_1, C_2)
polígono5, f', d', e' = Polygon(D', E', F')
j = OrthogonalLine(D', a)
k = OrthogonalLine(E', b)
l = OrthogonalLine(F', c)
m = OrthogonalLine(A, d')
n = OrthogonalLine(B, e')
p = OrthogonalLine(C, f')
Q = Intersect(k, l)
D = Intersect(p, n)
q = Circle(A, B, C)
X_{1114} = TriangleCenter(A, B, C, 1114)
E = Mirror(X_{1114}, r)
u = Vector(A, E)
s = Line(X_{155}, u)
a_1 = Line(X_{1114}, X_{1113})
c_1 = Circle(X_{155}, 4)
G = Intersect(c_1, t, 2)
w = Vector(X_{155}, G)
H = Intersect(c_1, s, 1)
z = Vector(X_{155}, H)

Tool: TrianguloETC
Dar el vértice A
Input: A_{etc}
Output: B_{etc}, C_{etc}, a, polígono1

c = Circle(A_{etc}, 13)
B_{etc} = Point(c)
d = Circle(A_{etc}, 9)
e = Circle(B_{etc}, 6)
C_{etc} = Intersect(d, e, 1)
polígono1, c_{etc}, a_{etc}, b_{etc} = Polygon(A_{etc}, B_{etc}, C_{etc})
a = Line(B_{etc}, C_{etc})

Tool: Coordenadas Trilineales (command CoordenadasTrilineales)
Dar los vértices de ABC y un  punto P
Input: A, B, C, P
Output: texto2, CoordTrilineales

q_1 = Segment(B, P)
e = Line(A, C)
E_1 = Intersect(e, q_1)
d = Line(C, B)
p_1 = Segment(A, P)
D_1 = Intersect(d, p_1)
ABC, c, a, b = Polygon(A, B, C)
e_1 = OrthogonalLine(P, a)
D = Intersect(e_1, d)
p = Segment(P, D)
α = If(Defined[D_1], -p, p)
f_1 = OrthogonalLine(P, b)
g = OrthogonalLine(P, c)
f = Line(A, B)
E = Intersect(f_1, e)
F = Intersect(g, f)
r_1 = Segment(P, C)
q = Segment(P, E)
r = Segment(P, F)
F_1 = Intersect(f, r_1)
β = If(Defined[E_1], -q, q)
γ = If(Defined[F_1], -r, r)
CoordTrilineales: {α, β, γ}
texto2: "" + CoordTrilineales + ""

Tool: Triangulo Pedal (command TrianguloPedal)
Dar ABC y P
Input: A, B, C, E
Output: polígono2, F, G, H

polígono1, c, a, b = Polygon(A, B, C)
e = OrthogonalLine(E, a)
f = OrthogonalLine(E, b)
g = OrthogonalLine(E, c)
h = Line(B, C)
i = Line(C, A)
j = Line(A, B)
F = Intersect(e, h)
G = Intersect(i, f)
H = Intersect(j, g)
polígono2, h_1, f_1, g_1 = Polygon(F, G, H)

Tool: Centro Ortologico (command CentroOrtologico)
Dar ABC y P
Input: A, B, C, P
Output: Q

B*

C*

polígono1, c, a, b = Polygon(A, B, C)
polígono2, A', B', C' = TrianguloPedal(A, B, C, P)
B_1 = Midpoint(b)
C_1 = Midpoint(c)
B_2 = Midpoint(C', A')
C_2 = Midpoint(B', A')
E' = Mirror(B_1, B_2)
F' = Mirror(C_1, C_2)
k = OrthogonalLine(E', b)
l = OrthogonalLine(F', c)
Q = Intersect(k, l)